Sustainable circular economy production system with emission control in LED bulb companies

Abstract Mother Earth has a completely sustainable circular life cycle pattern. In its life cycle, there is no harm created to any living creature or to the environment. In this paper, a sustainable circular economic production and consumption system in a led bulb firm that follows the same cycle pattern as our planet is developed. The circular economy concept, green technology, and carbon cap- and- trade policy is introduced in this model to control the carbon emission rate and resource depletion in LED firms. The profit function is maximized by Lagrange’s multipliers method and Karush-Kuhn-Tucker (KKT) criteria. The optimal order quantity and circularity index of the LED bulb are found for a wise production process. The concavity of the optimal profit function is proved by using the Hessian matrix method. Different linear and non-linear combinations of demand and profit functions were discussed. This article claims that the circularity level of LED bulbs has influenced their selling price, cost, and demand. The green technology and carbon cap and trade policy enhanced the sustainability of LED bulb companies. To get a clear understanding of the implication of this model in LED bulb companies the numerical examples, result in discussion and optimal solution table are provided. Sensitivity analysis is presented. Managerial implication explained in terms of arrived results. Limitations and possible future extensions of this model are given in the conclusion section.